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24 June, 05:09

The length of a rectangle is two more than four times the width if the perimeter is 54 inches what are the length and width?

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  1. 24 June, 06:59
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    Length = 22 inches, Width = 5 inches

    Step-by-step explanation:

    Let P represent the Perimeter, L, the length and W, the width

    Perimeter of a rectangle, P = 2 (L + W) ... eq 1

    from the question;

    L = 2 + 4W ... eq 2

    Slotting in the respective values of P and L in eq 1

    54 = 2{ (2 + 4W) + W}

    Expanding the bracket

    54 = 2 (2 + 5W)

    54 = 4 + 10W

    Subtracting 4 from both sides of the equation

    54 - 4 = 10 W

    50 = 10W

    Dividing both sides by the coefficient of W which is 10

    5 = W

    Therefore, W = 5 inches

    Slotting in the value of W in eq 2

    L = 2 + 4 (5)

    L = 2 + 20

    L = 22 inches

    Now lets check our answers by slotting in the values of P, L and W in eq 1

    54 = 2 (22 + 5)

    54 = 2 (27)

    54 = 54

    Since both sides of the equation are equal, the values of L and W are correct

    Hence Length = 22 inches, Width = 5 inches
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